Question 1. SHORT ANSWERS

10 citizens need to decide whether or not to revolt against their government. If at least 6 (i.e., n 6) citizens revolt against the government, they will start a successful revolution and overthrow the government. Otherwise (if n < 6), the government remains in power. The citizens' payoffs depend on whether they have chosen to revolt and whether the government is overthrown. Revolting is costly. Thus, if a citizen has chosen to revolt, their payoff is reduced by 5 regardless the outcome of the revolution. If the government is overthrown, each citizen receives payoff 10 regardless whether they have chosen to revolt or not, whereas if the government remains in power each citizen receives payoff 0. For example, if 8 citizens revolt, each of them will receive net payoff 5 and the other 2 citizens will each receive payoff 10. However, if 2 citizens revolt, each of them will receive net payoff -5 and the other 8 citizens will receive payoff 0.

a) Is every citizen revolting a Nash equilibrium of the game? Explain. b) Is every citizen not revolting a Nash equilibrium of the game? Explain. c) Are there any other Nash equilibria? If there are, specify such a Nash equilibrium, and verify that it is a Nash equilibrium. If no other Nash equilibria exit, explain why the other action profiles are not Nash equilibria.